Invariance principles for renewal processes when only moments of low order exist
TLDR
In this paper, Einmahl et al. developed corresponding invariance principles for associated renewal processes and random sums and proved the optimality of the approximation in the case when only two moments exist.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1988-08-01 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Renewal theory & Invariance principle.read more
Citations
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Anscombe's Theorem 60 Years Later
TL;DR: In this article, the main aim of the article is to illustrate the beauty and efficiency of what will be called the stopped random walk (SRW) method, and discuss the importance of this result and mention some of its impact, mainly on stopped random walks.
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Truncated Sequential Change‐point Detection based on Renewal Counting Processes
Allan Gut,Josef Steinebach +1 more
TL;DR: In this article, the authors consider the counting process related to the original process observed at equidistant time points, after which action is taken or not depending on the number of observations between those time points.
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Extreme Value Asymptotics for Multivariate Renewal Processes
TL;DR: In this article, a multivariate renewal process for a sequence of partial sums of d-dimensional independent identically distributed random vectors is defined componentwise, and a number of weak asymptotic results are established.
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Large deviations for renewal processes
TL;DR: In this article, the large deviation principle is established for a sequence of i.i.d. random variables, where the empty set is defined to be + ∞. But this is not the case when the sequence is an exchangeable sequence.
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Truncated sequential change-point detection based on renewal counting processes II
Allan Gut,Josef Steinebach +1 more
TL;DR: Gut and Steinebach as discussed by the authors studied the behaviour of relevant stopping times, in particular the time it takes from the actual change-point until the change is detected, more precisely, they proved asymptotics for stopping times under alternatives.
References
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An Approximation of Partial Sums of Independent RV's, and the Sample DF. II
TL;DR: In this article, the authors introduced a new construction for the pair S¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ n�, T¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ n>>\s, and proved that if X>>\s has a finite moment generating function, and satisfies condition i) or ii) of Theorem 1, then ¦S>>\s n� -T� n� nၡ 1/4(log n) 1/1(log log n)1/4) with probability one.
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An invariance principle for the law of the iterated logarithm.
Volker Strassen,Volker Strassen +1 more
TL;DR: In this paper, it was shown that with probability one the set of limit points of the sequence (ηn)n≧3 with respect to the uniform topology coincides with the sets of absolutely continuous functions x on "0, 1" such that x(0) = 0, 1, and ηn = 0 for any a ≧ 1.
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Approximation Thorems for Independent and Weakly Dependent Random Vectors
István Berkes,Walter Philipp +1 more
TL;DR: In this paper, approximation theorems of the following type were proved for sums of independent identically distributed random variables with values in Θ( √ √ n) with a logarithmic mixing rate.
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A limit theorem for the maximum of normalized sums of independent random variables
D. A. Darling,Paul Erdös +1 more
TL;DR: In this article, it was shown that the central limit theorem for U: = max,,,,, Sk/n+ is probably false if we drop the condition on t,he third absolut'e moment.